A need exists for high-speed modems, for example in modern broadband communication satellite systems, or their terrestrial equivalents. Another need is for very low-power modems, such as might find use in handheld communication receivers or in wireless computing devices. In addition, it is desirable to use as low a clock rate as possible relative to the symbol transmission rate in order to reduce power or so as to allow the use of a higher symbol rate with the same clock. By way of further example, clock rates at a given level of development of any given technology, such as silicon integrated circuits, gallium arsenide integrated circuits, or photonic devices, will have a finite upper frequency limit. At such a stage of development, the maximum symbol rate which can be handled by a modem will be determined, in the limit, by the number of complex samples per symbol required. Historically, the lowest practical sample per symbol rate has tended to be two complex samples per symbol. Therefore, the maximum symbol rate which a modem can handle is historically half the clock rate. In low-power applications, the symbol rate tends to be set by extrinsic standards, and therefore the clock rate is determined by the symbol rate and the number of complex samples per symbol. The power consumption is directly related to the clock rate, so a scheme which reduces the required clock rate for a given symbol rate will tend to reduce the power consumption.
Improved modems are desired.